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December, 2017 Analysis of a Stochastic Lotka-Volterra Competitive Model with Infinite Delay and Impulsive Perturbations
Chun Lu, Qiang Ma
Taiwanese J. Math. 21(6): 1413-1436 (December, 2017). DOI: 10.11650/tjm/8070

Abstract

This paper considers a stochastic Lotka-Volterra competitive model with infinite delay and impulsive perturbations. This model is new, more feasible and more accordance with the actual. The aim is to analyze what happens under the impulsive perturbations. With space $C_{g}$ as phase space, sufficient conditions for permanence in time average are established as well as extinction, stability in time average and global attractivity of each population. Numerical simulations are also exhibited to illustrate the validity of the results in this paper. In addition, a knowledge is given to illustrate that the statement in [21] is incorrect by choosing space $C_{g}$ as phase space. Our results demonstrate that impulsive perturbations which may represent human factor play a key role in protecting the population when environmental noise and interaction rates are disadvantageous to population survival.

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Chun Lu. Qiang Ma. "Analysis of a Stochastic Lotka-Volterra Competitive Model with Infinite Delay and Impulsive Perturbations." Taiwanese J. Math. 21 (6) 1413 - 1436, December, 2017. https://doi.org/10.11650/tjm/8070

Information

Received: 5 July 2016; Revised: 9 February 2017; Accepted: 9 April 2017; Published: December, 2017
First available in Project Euclid: 17 August 2017

zbMATH: 06871375
MathSciNet: MR3732912
Digital Object Identifier: 10.11650/tjm/8070

Subjects:
Primary: 34K45 , 60H40 , 92BXX , 93DXX

Keywords: environmental noise , impulsive perturbations , infinite delay , permanence in time average , stability

Rights: Copyright © 2017 The Mathematical Society of the Republic of China

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Vol.21 • No. 6 • December, 2017
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